Simplify √300
√300 = √(100 * 3) = √100 * √3 = 10√3
To simplify √300, we can find the prime factorization of 300 first.
Prime factorization of 300:
300 = 2 × 2 × 3 × 5 × 5
Now, we can simplify the square root using the prime factors:
√300 = √(2 × 2 × 3 × 5 × 5)
Since there are two pairs of the same prime factors (2 and 5), we can take them out of the square root sign:
= √(2^2 × 3 × 5^2)
Then, we can simplify the square root further:
= √(2^2) × √(3) × √(5^2)
= 2 × √(3) × 5
= 10√3
Therefore, the simplified form of √300 is 10√3.
To simplify the square root of 300, we need to find the largest perfect square that divides 300.
Let's start by listing the prime factors of 300:
300 = 2 × 2 × 3 × 5 × 5
Now, let's pair up the factors in pairs of two. Each pair will consist of a perfect square and any remaining factors:
300 = (2 × 2) × (3 × 5 × 5)
Simplifying further, we can write 300 as:
300 = 4 × 75
Since 4 is a perfect square (2 × 2 = 4), we can write the expression as:
√300 = √(4 × 75)
Now, we can simplify each individual square root:
√(4 × 75) = √4 × √75
The square root of 4 is 2, so we have:
2√75
Lastly, we need to check if 75 can be further simplified. Following the same process as before, we list the prime factors of 75:
75 = 3 × 5 × 5
Since there are no remaining factors that can be paired up, we can't simplify 75 any further.
Therefore, the simplified form of √300 is:
2√75
explain how?
Apologies for the confusion. Let's go through the simplification process again step by step:
We are trying to simplify the square root of 300: √300
First, we find the prime factorization of 300:
300 = 2 × 2 × 3 × 5 × 5
Next, we group the prime factors into pairs of two, with any remaining prime factors outside the square root:
300 = (2 × 2) × (3 × 5 × 5)
Now, we can simplify the terms within the square root by taking the square root of the perfect square:
√300 = √(4 × 75)
Taking the square root of 4 gives us 2:
√300 = 2√75
Now, let's focus on simplifying the remaining term √75.
To do this, we find the prime factorization of 75:
75 = 3 × 5 × 5
Since there are no remaining factors that can be paired up, we cannot simplify it any further.
Therefore, the simplified form of √300 is 2√75.